论文标题
一维扩散方程的基于多释放时间晶格Boltzmann模型的四级有限差分方案
A multiple-relaxation-time lattice Boltzmann model based four-level finite-difference scheme for one-dimensional diffusion equation
论文作者
论文摘要
在本文中，我们首先提出了一维扩散方程的多余时间晶格Boltzmann（MRT-LB）模型，其中考虑了D1Q3（一维空间中的三个离散速度）晶格结构。然后，通过理论分析，我们从此MRT-LB模型中得出了一个明确的四级有限差分方案。结果表明，四级有限差分方案是无条件稳定的，并且通过调整重量系数$ω_{0} $和放松参数$ s_1 $和$ s_2 $，与第一和第二瞬间相对应，它也可以在空间中具有第六阶准确度。最后，我们还通过一些数值模拟测试了四级有限差异方案，并发现数值结果与我们的理论分析一致。
In this paper, we first present a multiple-relaxation-time lattice Boltzmann (MRT-LB) model for one-dimensional diffusion equation where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is considered. Then through the theoretical analysis, we derive an explicit four-level finite-difference scheme from this MRT-LB model. The results show that the four-level finite-difference scheme is unconditionally stable, and through adjusting the weight coefficient $ω_{0}$ and the relaxation parameters $s_1$ and $s_2$ corresponding to the first and second moments, it can also have a sixth-order accuracy in space. Finally, we also test the four-level finite-difference scheme through some numerical simulations, and find that the numerical results are consistent with our theoretical analysis.
